A First Course in Linear Algebra · Problem CRS.C34

Matrices — Robert Beezer

Mathematics — Linear Algebra · row-space-membership

Problem

For the

3 \times 4

matrix

A

and the column vector

\mathbf{y} \in \mathbb{C}^4

given below, determine if

\mathbf{y}

is in the row space of

A

. In other words, answer the question:

\mathbf{y} \in \mathcal{R}(A)

A = \begin{bmatrix} -2 & 6 & 7 & -1 \\ 7 & -3 & 0 & -3 \\ 8 & 0 & 7 & 6 \end{bmatrix} \qquad \mathbf{y} = \begin{bmatrix} 2 \\ 1 \\ 3 \\ -2 \end{bmatrix}